Foliations on Riemannian Manifolds:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
New York, NY
Springer New York
1988
|
| Schriftenreihe: | Universitext
|
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | A first approximation to the idea of a foliation is a dynamical system, and the resulting decomposition of a domain by its trajectories. This is an idea that dates back to the beginning of the theory of differential equations, i.e. the seventeenth century. Towards the end of the nineteenth century, Poincare developed methods for the study of global, qualitative properties of solutions of dynamical systems in situations where explicit solution methods had failed: He discovered that the study of the geometry of the space of trajectories of a dynamical system reveals complex phenomena. He emphasized the qualitative nature of these phenomena, thereby giving strong impetus to topological methods. A second approximation is the idea of a foliation as a decomposition of a manifold into submanifolds, all being of the same dimension. Here the presence of singular submanifolds, corresponding to the singularities in the case of a dynamical system, is excluded. This is the case we treat in this text, but it is by no means a comprehensive analysis. On the contrary, many situations in mathematical physics most definitely require singular foliations for a proper modeling. The global study of foliations in the spirit of Poincare was begun only in the 1940's, by Ehresmann and Reeb |
| Beschreibung: | 1 Online-Ressource (XI, 247p. 7 illus) |
| ISBN: | 9781461387800 9780387967073 |
| ISSN: | 0172-5939 |
| DOI: | 10.1007/978-1-4613-8780-0 |
Internformat
MARC
| LEADER | 00000nmm a2200000zc 4500 | ||
|---|---|---|---|
| 001 | BV042420752 | ||
| 003 | DE-604 | ||
| 005 | 00000000000000.0 | ||
| 007 | cr|uuu---uuuuu | ||
| 008 | 150317s1988 |||| o||u| ||||||eng d | ||
| 020 | |a 9781461387800 |c Online |9 978-1-4613-8780-0 | ||
| 020 | |a 9780387967073 |c Print |9 978-0-387-96707-3 | ||
| 024 | 7 | |a 10.1007/978-1-4613-8780-0 |2 doi | |
| 035 | |a (OCoLC)879623991 | ||
| 035 | |a (DE-599)BVBBV042420752 | ||
| 040 | |a DE-604 |b ger |e aacr | ||
| 041 | 0 | |a eng | |
| 049 | |a DE-384 |a DE-703 |a DE-91 |a DE-634 | ||
| 082 | 0 | |a 514.34 |2 23 | |
| 084 | |a MAT 000 |2 stub | ||
| 100 | 1 | |a Tondeur, Philippe |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Foliations on Riemannian Manifolds |c by Philippe Tondeur |
| 264 | 1 | |a New York, NY |b Springer New York |c 1988 | |
| 300 | |a 1 Online-Ressource (XI, 247p. 7 illus) | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b c |2 rdamedia | ||
| 338 | |b cr |2 rdacarrier | ||
| 490 | 0 | |a Universitext |x 0172-5939 | |
| 500 | |a A first approximation to the idea of a foliation is a dynamical system, and the resulting decomposition of a domain by its trajectories. This is an idea that dates back to the beginning of the theory of differential equations, i.e. the seventeenth century. Towards the end of the nineteenth century, Poincare developed methods for the study of global, qualitative properties of solutions of dynamical systems in situations where explicit solution methods had failed: He discovered that the study of the geometry of the space of trajectories of a dynamical system reveals complex phenomena. He emphasized the qualitative nature of these phenomena, thereby giving strong impetus to topological methods. A second approximation is the idea of a foliation as a decomposition of a manifold into submanifolds, all being of the same dimension. Here the presence of singular submanifolds, corresponding to the singularities in the case of a dynamical system, is excluded. This is the case we treat in this text, but it is by no means a comprehensive analysis. On the contrary, many situations in mathematical physics most definitely require singular foliations for a proper modeling. The global study of foliations in the spirit of Poincare was begun only in the 1940's, by Ehresmann and Reeb | ||
| 650 | 4 | |a Mathematics | |
| 650 | 4 | |a Cell aggregation / Mathematics | |
| 650 | 4 | |a Manifolds and Cell Complexes (incl. Diff.Topology) | |
| 650 | 4 | |a Mathematik | |
| 650 | 0 | 7 | |a Blätterung |0 (DE-588)4007006-2 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Riemannscher Raum |0 (DE-588)4128295-4 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Blätterung |0 (DE-588)4007006-2 |D s |
| 689 | 0 | 1 | |a Riemannscher Raum |0 (DE-588)4128295-4 |D s |
| 689 | 0 | |8 1\p |5 DE-604 | |
| 856 | 4 | 0 | |u https://doi.org/10.1007/978-1-4613-8780-0 |x Verlag |3 Volltext |
| 912 | |a ZDB-2-SMA |a ZDB-2-BAE | ||
| 940 | 1 | |q ZDB-2-SMA_Archive | |
| 999 | |a oai:aleph.bib-bvb.de:BVB01-027856169 | ||
| 883 | 1 | |8 1\p |a cgwrk |d 20201028 |q DE-101 |u https://d-nb.info/provenance/plan#cgwrk | |
Datensatz im Suchindex
| _version_ | 1804153093046140928 |
|---|---|
| any_adam_object | |
| author | Tondeur, Philippe |
| author_facet | Tondeur, Philippe |
| author_role | aut |
| author_sort | Tondeur, Philippe |
| author_variant | p t pt |
| building | Verbundindex |
| bvnumber | BV042420752 |
| classification_tum | MAT 000 |
| collection | ZDB-2-SMA ZDB-2-BAE |
| ctrlnum | (OCoLC)879623991 (DE-599)BVBBV042420752 |
| dewey-full | 514.34 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 514 - Topology |
| dewey-raw | 514.34 |
| dewey-search | 514.34 |
| dewey-sort | 3514.34 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| doi_str_mv | 10.1007/978-1-4613-8780-0 |
| format | Electronic eBook |
| fullrecord | <?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>02948nmm a2200481zc 4500</leader><controlfield tag="001">BV042420752</controlfield><controlfield tag="003">DE-604</controlfield><controlfield tag="005">00000000000000.0</controlfield><controlfield tag="007">cr|uuu---uuuuu</controlfield><controlfield tag="008">150317s1988 |||| o||u| ||||||eng d</controlfield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9781461387800</subfield><subfield code="c">Online</subfield><subfield code="9">978-1-4613-8780-0</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9780387967073</subfield><subfield code="c">Print</subfield><subfield code="9">978-0-387-96707-3</subfield></datafield><datafield tag="024" ind1="7" ind2=" "><subfield code="a">10.1007/978-1-4613-8780-0</subfield><subfield code="2">doi</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(OCoLC)879623991</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-599)BVBBV042420752</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-604</subfield><subfield code="b">ger</subfield><subfield code="e">aacr</subfield></datafield><datafield tag="041" ind1="0" ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="049" ind1=" " ind2=" "><subfield code="a">DE-384</subfield><subfield code="a">DE-703</subfield><subfield code="a">DE-91</subfield><subfield code="a">DE-634</subfield></datafield><datafield tag="082" ind1="0" ind2=" "><subfield code="a">514.34</subfield><subfield code="2">23</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">MAT 000</subfield><subfield code="2">stub</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Tondeur, Philippe</subfield><subfield code="e">Verfasser</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Foliations on Riemannian Manifolds</subfield><subfield code="c">by Philippe Tondeur</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="a">New York, NY</subfield><subfield code="b">Springer New York</subfield><subfield code="c">1988</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">1 Online-Ressource (XI, 247p. 7 illus)</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="b">c</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="b">cr</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="490" ind1="0" ind2=" "><subfield code="a">Universitext</subfield><subfield code="x">0172-5939</subfield></datafield><datafield tag="500" ind1=" " ind2=" "><subfield code="a">A first approximation to the idea of a foliation is a dynamical system, and the resulting decomposition of a domain by its trajectories. This is an idea that dates back to the beginning of the theory of differential equations, i.e. the seventeenth century. Towards the end of the nineteenth century, Poincare developed methods for the study of global, qualitative properties of solutions of dynamical systems in situations where explicit solution methods had failed: He discovered that the study of the geometry of the space of trajectories of a dynamical system reveals complex phenomena. He emphasized the qualitative nature of these phenomena, thereby giving strong impetus to topological methods. A second approximation is the idea of a foliation as a decomposition of a manifold into submanifolds, all being of the same dimension. Here the presence of singular submanifolds, corresponding to the singularities in the case of a dynamical system, is excluded. This is the case we treat in this text, but it is by no means a comprehensive analysis. On the contrary, many situations in mathematical physics most definitely require singular foliations for a proper modeling. The global study of foliations in the spirit of Poincare was begun only in the 1940's, by Ehresmann and Reeb</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Mathematics</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Cell aggregation / Mathematics</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Manifolds and Cell Complexes (incl. Diff.Topology)</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Mathematik</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Blätterung</subfield><subfield code="0">(DE-588)4007006-2</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Riemannscher Raum</subfield><subfield code="0">(DE-588)4128295-4</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="689" ind1="0" ind2="0"><subfield code="a">Blätterung</subfield><subfield code="0">(DE-588)4007006-2</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2="1"><subfield code="a">Riemannscher Raum</subfield><subfield code="0">(DE-588)4128295-4</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2=" "><subfield code="8">1\p</subfield><subfield code="5">DE-604</subfield></datafield><datafield tag="856" ind1="4" ind2="0"><subfield code="u">https://doi.org/10.1007/978-1-4613-8780-0</subfield><subfield code="x">Verlag</subfield><subfield code="3">Volltext</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">ZDB-2-SMA</subfield><subfield code="a">ZDB-2-BAE</subfield></datafield><datafield tag="940" ind1="1" ind2=" "><subfield code="q">ZDB-2-SMA_Archive</subfield></datafield><datafield tag="999" ind1=" " ind2=" "><subfield code="a">oai:aleph.bib-bvb.de:BVB01-027856169</subfield></datafield><datafield tag="883" ind1="1" ind2=" "><subfield code="8">1\p</subfield><subfield code="a">cgwrk</subfield><subfield code="d">20201028</subfield><subfield code="q">DE-101</subfield><subfield code="u">https://d-nb.info/provenance/plan#cgwrk</subfield></datafield></record></collection> |
| id | DE-604.BV042420752 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T01:21:07Z |
| institution | BVB |
| isbn | 9781461387800 9780387967073 |
| issn | 0172-5939 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-027856169 |
| oclc_num | 879623991 |
| open_access_boolean | |
| owner | DE-384 DE-703 DE-91 DE-BY-TUM DE-634 |
| owner_facet | DE-384 DE-703 DE-91 DE-BY-TUM DE-634 |
| physical | 1 Online-Ressource (XI, 247p. 7 illus) |
| psigel | ZDB-2-SMA ZDB-2-BAE ZDB-2-SMA_Archive |
| publishDate | 1988 |
| publishDateSearch | 1988 |
| publishDateSort | 1988 |
| publisher | Springer New York |
| record_format | marc |
| series2 | Universitext |
| spelling | Tondeur, Philippe Verfasser aut Foliations on Riemannian Manifolds by Philippe Tondeur New York, NY Springer New York 1988 1 Online-Ressource (XI, 247p. 7 illus) txt rdacontent c rdamedia cr rdacarrier Universitext 0172-5939 A first approximation to the idea of a foliation is a dynamical system, and the resulting decomposition of a domain by its trajectories. This is an idea that dates back to the beginning of the theory of differential equations, i.e. the seventeenth century. Towards the end of the nineteenth century, Poincare developed methods for the study of global, qualitative properties of solutions of dynamical systems in situations where explicit solution methods had failed: He discovered that the study of the geometry of the space of trajectories of a dynamical system reveals complex phenomena. He emphasized the qualitative nature of these phenomena, thereby giving strong impetus to topological methods. A second approximation is the idea of a foliation as a decomposition of a manifold into submanifolds, all being of the same dimension. Here the presence of singular submanifolds, corresponding to the singularities in the case of a dynamical system, is excluded. This is the case we treat in this text, but it is by no means a comprehensive analysis. On the contrary, many situations in mathematical physics most definitely require singular foliations for a proper modeling. The global study of foliations in the spirit of Poincare was begun only in the 1940's, by Ehresmann and Reeb Mathematics Cell aggregation / Mathematics Manifolds and Cell Complexes (incl. Diff.Topology) Mathematik Blätterung (DE-588)4007006-2 gnd rswk-swf Riemannscher Raum (DE-588)4128295-4 gnd rswk-swf Blätterung (DE-588)4007006-2 s Riemannscher Raum (DE-588)4128295-4 s 1\p DE-604 https://doi.org/10.1007/978-1-4613-8780-0 Verlag Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Tondeur, Philippe Foliations on Riemannian Manifolds Mathematics Cell aggregation / Mathematics Manifolds and Cell Complexes (incl. Diff.Topology) Mathematik Blätterung (DE-588)4007006-2 gnd Riemannscher Raum (DE-588)4128295-4 gnd |
| subject_GND | (DE-588)4007006-2 (DE-588)4128295-4 |
| title | Foliations on Riemannian Manifolds |
| title_auth | Foliations on Riemannian Manifolds |
| title_exact_search | Foliations on Riemannian Manifolds |
| title_full | Foliations on Riemannian Manifolds by Philippe Tondeur |
| title_fullStr | Foliations on Riemannian Manifolds by Philippe Tondeur |
| title_full_unstemmed | Foliations on Riemannian Manifolds by Philippe Tondeur |
| title_short | Foliations on Riemannian Manifolds |
| title_sort | foliations on riemannian manifolds |
| topic | Mathematics Cell aggregation / Mathematics Manifolds and Cell Complexes (incl. Diff.Topology) Mathematik Blätterung (DE-588)4007006-2 gnd Riemannscher Raum (DE-588)4128295-4 gnd |
| topic_facet | Mathematics Cell aggregation / Mathematics Manifolds and Cell Complexes (incl. Diff.Topology) Mathematik Blätterung Riemannscher Raum |
| url | https://doi.org/10.1007/978-1-4613-8780-0 |
| work_keys_str_mv | AT tondeurphilippe foliationsonriemannianmanifolds |